Question

their twenty-fifth anniversary if Anthony and Michelle Constantino just got married and received $30,000 in cash gifts for their wedding. How much will they have on they place half of this money in a fixed-rate investment earning 10 percent compounded annually? Would the future value be larger or smaller if the compounding period was 6 months? How much more or less would they have earned with this shorter compounding period? Click on the table icon to view the FVIF table f they place half of this money, PV in a fixed rate investment earning 10 percent compounded annually, the amount they wil have. FV, on their twenty-fth anniversary is(Round to the nearest cent.)

Answer 1

Total Gifts Received in Cash = $ 30000, Amount Put into Savings = 0.5 x 30000 = $ 15000

Rate of Interest = 10 %, Tenure = 25 years and Frequency of compounding = Annual

Therefore, Total Future Value = 15000 x (1.1)^(25) = $ 162520.59

If the compounding is done twice a year (6 months compounding period), then the total future value of the savings would be higher as the money deposited earns interest twice the number of times as compared to annual compounding.

Semi-Annual Interest Rate = (10/2) = 5 % and Semi-Annual Periods = 25 x 2 = 50

Therefore, Total Future Value = 15000 x (1.05)^(50) = $ 172010.99

Extra Money Earned by using 6 month compounding = 172010.99 - 162520.59 = $ 9490.41